The cop who gunned down an unarmed teen on a Brooklyn rooftop is defending himself by saying the shooting was a split-second reaction to a door springing open – and it happened so fast he never even realized he fired, sources said yesterday.

Officer Richard Neri, 35, has told those close to him that early Saturday morning, he and his partner, Officer Jason Hallik, were on the roof of the building at the Louis Armstrong Houses about to enter the stairwell when the door sprung open as Hallik was reaching to pull it open.

The motion caused Hallik, a four-year veteran, to be thrown back.

Neri said it was reflex that prompted him to fire at a lone figure, Timothy Stansbury Jr., 19, standing in the doorway.

Although Neri reportedly told Hallik, “I let one go,” the cop still doesn’t remember lifting up his 9 mm Glock or pointing it.

“He knows he fired the shot, but the last thing he remembers his gun was at his side,” one source said.

Neri said he and his partner were conducting a “vertical patrol” on the roof and had their guns drawn at their sides at the time – something Neri said he was taught to do more than 11 years ago, when he first joined the housing wing of the NYPD.

“From his first day [in housing], he was trained [that] when you do vertical patrols [stairway patrols], you have your weapon out by your side,” a source said Neri told him.

The practice, exercised by some housing officers, is not prohibited by the department, but is now under review by an internal panel established by Police Commissioner Ray Kelly yesterday and will be part of an upcoming grand jury investigation, sources said.

Neri, who’s been placed on modified assignment, spent most of yesterday holed up at his Wantagh, L.I., home.

When a reporter asked him to relate his story, the cop mumbled, “No comment,” and walked toward the ranch-style house he shares with his pregnant wife and two children.

Meanwhile yesterday, investigators for the Brooklyn district attorney met with two eyewitnesses to the shooting.

DA Charles Hynes met with Stansbury’s parents, who called for the cop to “go to jail.”

One City Hall source, asked if the city would pay for the tragic teen’s funeral, said: “We haven’t been asked yet. But if we were, I imagine we’d pay for it.”